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![Measurements of the beam radius, ω\documentclass[12pt]{minimal}...](publication/365256286/figure/fig5/AS:11431281098417051@1668912976140/Measurements-of-the-beam-radius-odocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
A three-point Focused Laser Differential Interferometer (FLDI) instrument was implemented to investigate the freestream disturbance environment in a Mach-6 shock tunnel. The FLDI beams were split such that one pair was aligned with the flow direction and the other along the Mach angle, allowing for simultaneous measurements of entropic fluctuations...
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The characterization of a hypersonic impulse facility is performed using a variety of methods including Pitot probe scans, particle image velocimetry, and schlieren imaging to verify properties such as the velocity, Mach number, wall boundary layer thickness, and freestream turbulence intensity levels. The experimental results are compared to the n...
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... Since traditional FLDI is limited to a single point, spatially resolved information can only be obtained by using physical scanning [6,15], which can be time-consuming and unreliable as test conditions can vary over time. Recently, two-point, three-point, linear array, grid, and line-based FLDI setups have been developed to capture multiple spatial locations simultaneously [16][17][18]. However, these methods can require custom diffractive optics and multiple photodiodes, which significantly increases the setup complexity. ...
Focused laser differential interferometry (FLDI) is an important diagnostic for measuring density fluctuations in high-speed flows. Currently, however, high dynamic range FLDI is limited to photodiode measurements. In order to spatially resolve multiple locations within complex flows, we present a novel, to the best of our knowledge, refractive-optic imaging FLDI concept that not only produces two-dimensional images without scanning but also reduces the measurement noise floor of those images. To demonstrate this concept, a 33 × 33 grid of FLDI points is first generated using a microlens array. Then, the beams are split and recombined using two polarized Mach–Zehnder interferometers to maximize flexibility in beam separation and optimize signal sensitivity. Next, the FLDI points are collected slightly out of focus on a high-speed camera in order to increase the number of pixels n per FLDI point, thereby reducing noise floor by $\mathrm {\mathbf {\sqrt {n}}}$ n . Finally, an under-expanded jet with a characteristic screech at 14.1 kHz is tested with the imaging FLDI setup, showing clear barrel and reflected shock features as well as spatially varying turbulence densities. Overall, this unique concept enables the creation of reduced-noise-floor, two-dimensional FLDI datasets for the study of supersonic and hypersonic flows.
... This value is typically between 3 and 10 lm for other FLDI setups in the literature. 74,77,79,80 Using this value, we calculate the transfer function and evaluate it at k ¼ 2:5 mm, which predicts the FLDI depth-of-field at the relevant second mode frequency. It is plotted as the green curve in Fig. 4(a). ...
Hypersonic boundary-layer transition onset is commonly characterized in wind tunnel experiments by measuring the surface heat transfer rise above the laminar level. Techniques such as infrared thermography and thin film gauges are routinely used in the field. However, when an interfering cooling effect is present due to foreign gas transpiration, these methods are known to be inadequate. This study uses a 7 half-angle cone at Mach 7 with helium or nitrogen injection through a porous segment within the model frustum. The injector spans 60 in azi-muth and is located 300 mm from the sharp nose tip, close to the onset of natural boundary-layer transition. Nitrogen and helium injection reduce the surface heat flux below the laminar level for up to 50 mm downstream of the injector. Comparisons to schlieren images and pressure measurements indicate an advance of transition. Optical diagnostics reveal how instabilities are pushed away from the model surface by the injected gas. This is found through spectral analysis of schlieren images and focused laser differential interferometry signals, which revealed further information about how inaccuracies of detecting transition with surface gauges under the influence of transpiration cooling originate.
... The signals were then digitized by a 14-bit Picoscope 5444D and sampled at 25 MHz. The relationship between the output voltage, measured phase change, and density gradient is outlined in Gillespie et al. (2022). ...
... Low-wavenumber disturbances, however, may still be corrupted by sidewall boundary layers, while high wavenumbers are more representative of disturbances in the core flow region. Gillespie et al. (2022) present an analysis of this signal attenuation for a similar four-point FLDI in the Mach-6 configuration of the HyperTERP facility. An important parameter used when determining the influence of the sidewall boundary layers on the measured signal is the Gaussian beam radius, . ...
... Following the procedure detailed in Sect. 3.5 of Gillespie et al. (2022), a cutoff wavenumber is conservatively estimated, whereby disturbances with larger wavenumbers can be attributed to the core flow. In addition to properties of the FLDI ( 0 , 0 , Δx 1 ), the calculation of the cutoff wavenumber is dependent on the sidewall boundary-layer thickness, half-width of the flow region (25.4 mm), and the ratio of frequency-averaged disturbance amplitudes of the sidewall boundary layers relative to the core flow. ...
The effects of vibrational nonequilibrium processes on turbulence-generated acoustic noise were investigated in a Mach-2.8 shock-tunnel facility. Gas mixtures with relevant absorption characteristics were first identified from measurements of attenuation coefficients using a heated acoustic chamber. In the shock-tunnel facility, CO\(_2\), N\(_2\), He, and He/CO\(_2\) mixtures were injected into the lower boundary layer of the flow through a porous plate. A four-point Focused Laser Differential Interferometer (FLDI) positioned above the turbulent boundary layer was used to obtain simultaneous freestream measurements of entropic fluctuations propagating along streamlines and acoustic disturbances along Mach lines. Correlated fluctuations of Mach-line and streamline FLDI signal pairs were analyzed with a cross-power spectral density (CPSD). Compared to a boundary layer of pure air, the injection of 30%, 35%, and 40% He/CO\(_2\) mixtures resulted in reduced fluctuation powers correlated along a Mach line in the frequency range of 200–800 kHz. Minimal reductions in fluctuation power were found along a streamline, indicating that the vibrationally active gas is affecting acoustic disturbances and not entropic disturbances. A mathematical disturbance model was created to examine the sensitivity of the measured attenuation to acoustic disturbances propagating from the lower boundary layer only. Disturbances were modeled as Gaussian wave packets of finite width, propagating in the streamwise direction and along Mach lines from the four walls of the test section. Modeling the acoustic disturbances from the lower boundary layer with a 15–30% amplitude reduction resulted in amplitude spectral densities and CPSDs that agreed well with the FLDI measurements.
... The model of study is a 7-degree half-angle cone instrumented with surface pressure sensors, thin film heat transfer gauges (TFGs), and an interchangeable nose tip [22,23]. The start of transition is experimentally determined from the TFGs, the boundary and entropy layer flow-field is interrogated with high-speed schlieren visualizations, and the freestream disturbance environment is characterized with multi-point focused laser differential interferometry (FLDI) [8,[24][25][26][27][28][29]. ...
... These disturbances are convecting at velocities less than or equal to the freestream, therefore their contribution to the FLDI signal is restricted to frequencies less than a cut-off. A method for estimating this cut-off frequency is proposed by Ceruzzi [45] and was recently employed by Gillespie et al. [27]. A simplified version of this method is employed here: Assuming disturbances are primarily flow-parallel and convecting with velocity ( ) along the stream-wise axis (x), the variation in FLDI sensitivity along the optical axis ( ) will only be a function of the transfer function, , given by Eq.28 from Ceruzzi and Cadou [25]: ...
... Turbulence intensity is computed from the spectra by integrating the the PSDs from [195 − 605] , (using MATLAB's trapz function) and taking the square-root of the result. This operation is completed for each channel and the median value is plotted vs Reynolds number in Fig.12 along with a comparison to FLDI-based turbulence intensity measured by Gillespie et al. [27]. The data from Gillespie et al. [27] is re-scaled (by a factor of 3.6) such that a logarithmic fit to the data crosses through the measurements made in this work. ...
Boundary layer instabilities and transition to turbulence on a 7-degree half-angle cone with varying nose-tip radii in Mach 6 and 7 flow are investigated using a combination of surface heat transfer measurements, surface pressure measurements, and high speed schlieren images. The experiments are performed at unit-Reynolds numbers ranging from [22 − 44] × 10 6 /m in University of Oxford's High-Density Tunnel (HDT). The transition Reynolds number, , increases with increasing nose tip Reynolds number, , for ≤ 10 5. In this range, evidence of second-mode wave instabilities are observed in both schlieren images and surface pressure measurements. For 10 5 < < 4 × 10 5 , remains constant and coherent streaks above the boundary layer are observed with schlieren imaging. Images of the interaction of these features with a boundary layer breaking down to a fully turbulent state are presented. The freestream disturbance environment is also varied through existence of several steady state plateaus created by the natural operation of the facility, and characterised with multi-point focused laser differential interferometry (FLDI). increases by ∼ 10 − 60% with increasing plateau number which is independent of. Variation in freestream fluctuation amplitude with frequency and Reynolds number are in agreement with previous studies while variation with plateau is not. The discrepancy is explained by receptivity functions which are sensitive to the inclination angle of disturbances. A method for measuring the inclination angle using correlated FLDI signals is presented and reveals a consistent trend with plateau number. The trend is physically explained by changes in the relative contribution of entropic and acoustic modes with time. I. Nomenclature = speed of sound = specific heat capacity = frequency = FLDI beam radius transfer function ì = disturbance wave-vector = integration length = Mach number = relative Mach number = pressure = heat flux = recovery factor = cross-correlation = Reynolds number = nose radius = Stanton number
... An entropy disturbance with a characteristic frequency of 3-4 kHz was identified, which had not been detected through pitot pressure measurement thus far. Gillespie et al. 12 conducted experimental research on hypersonic freestream disturbances along streamlines and Mach lines using the multi-point FLDI technique and the density fluctuation spectrum exhibited a roll-off of f À1:87 . Lawson et al. 13 conducted experiments to compare the freestream fluctuation spectra by the FLDI and pitot-pressure. ...
In this study, experimental investigations pertaining to aerodynamic noise are conducted in a hypersonic quiet wind tunnel, which possesses the unique capability of operating in both quiet and conventional modes, achieved by controlling the bleed slot to regulate the boundary layer flow. The measurement of aerodynamic noise and analysis of coherent structures of hypersonic turbulence are accomplished employing pressure probes and the nano-tracer-based planar laser scattering technique. The characterization of aerodynamic noise within the freestream unveils that noise generated by turbulent structures on the nozzle wall is the primary factor affecting the turbulence intensity of the freestream flow. Regarding the acoustic radiation noise generated by the turbulence on the nozzle wall, a peak frequency ranging from 54 to 57 kHz is observed in its spectrum within a unit Reynolds number range of 0.3×107–1.1×107 m−1. Under different operation modes, the freestream pitot-pressure data feature the similar spectral slope of f−2.2 and f−12 before and after the aforementioned peak. Through wavelet analysis, scales of the coherent structure in the turbulent boundary layer are examined, revealing that the maximum energy streamwise scale of the coherent structure is approximately 2.47 mm under the unit Reynolds number of 0.7×107 m−1. The product of this scale with the characteristic frequency of 56 kHz obtained from fluctuating pressure measurements is close to the local sound speed of about 140 m/s.
... The plotted straight line with a slope of −3.5, which appears to describe the current data quite well in the frequency range above ≈50 kHz, is consistent not only with the roll-off of the Pitot-pressure spectra from numerous previous studies in conventional hypersonic wind tunnels (see review in Ref. [17]), but also with the roll-off found in previously published FLDI freestream spectra in comparable lowenthalpy hypersonic tunnels [16,18]. ...
... It is commonly agreed that the main source for free flow disturbances in conventional supersonic and hypersonic wind tunnels is the radiation of acoustic waves from the turbulent boundary layer at the wind tunnel walls into the measurement section [19][20][21]. Accordingly, the measured shape of the PSD spectrum (Fig. 9b) is consistent with the FLDI results from other wind tunnels [16,18]. A comparison regarding the amplitude of the freestream disturbances is void, since the absolute value of the optical phase difference (Δs) depends on the individual measurement setup, and thus the prerequisite for an objective evaluation is missing. ...
... A comparison regarding the amplitude of the freestream disturbances is void, since the absolute value of the optical phase difference (Δs) depends on the individual measurement setup, and thus the prerequisite for an objective evaluation is missing. Although the laser beams are expanded as they traverse the nozzle boundary layer and thus primarily highfrequency signals are attenuated, studies [4,18,22] showed that the measurement signal may also contain shares of the low frequency density fluctuations from the nozzle boundary layer. (Fig. 10a), the growth of the perturbations due to the laminarturbulent transition at the flat plate becomes visible and leads to a broader frequency spectrum. ...
A new approach for measuring boundary-layer disturbances with focused laser differential interferometry (FLDI) for planar models is presented. By integrating a glass window into a flat plate, the optical axis was aligned normal to the model surface, and the focal plane was set inside the boundary layer. By determining the extent of the sensitive volume along the optical axis and calculating the analytical transfer function of the setup, the implications of the FLDI properties on the measured data are analyzed. Measurements performed on a flat plate at Mach 6 are used to demonstrate the effects of the laminar–turbulent transition on the spectral distribution of the power density and to explicitly verify the detectability of the expected second-mode instabilities. Advantages and disadvantages of the proposed setup compared to the conventional one are discussed.
... The signals were then digitized by a 14-bit Picoscope 5444D and sampled at 25 MHz. The relationship between the output voltage, measured phase change and density gradient is outlined in Gillespie et al. (2022). ...
... Low-wavenumber disturbances, however, may still be corrupted by sidewall boundary layers, while high wavenumbers are more representative of disturbances in the core flow region. Gillespie et al. (2022) presents an analysis of this signal attenuation for a similar four-point FLDI in the Mach-6 configuration of the HyperTERP facility. An important parameter used when determining the influence of the sidewall boundary layers on the measured signal is the Gaussian beam radius, ω. ...
... To do so, the FLDI sensitivity transfer function developed by Ceruzzi and Cadou (2022) was applied to the four-point FLDI setup. Following the procedure outlined by Gillespie et al. (2022), a cutoff wavenumber is conservatively estimated, whereby disturbances with larger wavenumbers can be attributed to the core flow. In addition to properties of the FLDI (λ 0 , ω 0 , ∆x 1 ), the calculation of the cutoff wavenumber is dependent on the sidewall boundary-layer thickness, half-width of the flow region (25.4 mm), and the ratio of frequency-averaged disturbance amplitudes of the sidewall boundary layers relative to the core flow. ...
The effects of vibrational nonequilibrium processes on turbulence-generated acoustic noise were investigated in a Mach-2.8 shock-tunnel facility. Gas mixtures with relevant absorption characteristics were first identified from measurements of attenuation coefficients using a heated acoustic chamber. In the shock-tunnel facility, CO2, N2, He, and He/CO2 mixtures were injected into the lower boundary layer of the flow through a porous plate. A four-point Focused Laser Differential Interferometer (FLDI) positioned above the turbulent boundary layer was used to obtain simultaneous freestream measurements of entropic fluctuations propagating along streamlines and acoustic disturbances along Mach lines. Correlated fluctuations of Mach-line and streamline FLDI signal pairs were analyzed with a cross power spectral density (CPSD). Compared to a boundary layer of pure air, the injection of 30%, 35%, and 40% He/CO2 mixtures resulted in reduced fluctuation powers correlated along a Mach line in the frequency range of 200-800 kHz. Minimal reductions in fluctuation power were found along a streamline, indicating that the vibrationally active gas is affecting acoustic disturbances and not entropic disturbances. A mathematical disturbance model was created to examine the sensitivity of the measured attenuation to acoustic disturbances propagating from the lower boundary layer only. Disturbances were modeled as Gaussian wave packets of finite width, propagating in the streamwise direction and along Mach lines from the four walls of the test section. Modeling the acoustic disturbances from the lower boundary layer with a 15-30% amplitude reduction resulted in amplitude spectral densities and CPSDs that agreed well with the FLDI measurements.
... The entropy and vorticity modes convect as frozen patterns along streamlines, while the acoustic modes can cross streamlines and do not convect as a frozen pattern with the local mean velocity. Shock tunnel free stream disturbances have been demonstrated to be mainly acoustic [9][10][11], and to convect with a Mach-number-dependent ratio with respect to the free stream [4,12]. No general rule for such dependence has yet been proposed, and the compilation of a database to support this is still underway. ...
... FLDI is a non-intrusive technique capable of measuring flowfield density disturbances along a line-of-sight with an extreme bandwidth and increased sensitivity near the focal plane [32,33]. These characteristics make FLDI a powerful measurement technique for shock tunnel investigations, with many researchers having employed it to probe the free stream [10,11,[34][35][36] and laminar boundary layers [37][38][39][40][41][42][43]. Nonetheless, the application of the technique to hypersonic turbulent boundary layers remains largely unexplored. ...
... It is such that high-frequency content is only detected near the center plane, but the lower end of the spectrum is detected along the entire optical axis. Therefore, the shear layer imposes a lower limit on the useful frequency response of the FLDI, below which the measurements are dominated by shear layer content [11,52]. However, the limit is not a well-defined value, as the FLDI response to a disturbance of a given wavenumber rolls off continuously away from the center plane. ...
This work investigates a hypersonic turbulent boundary layer over a 7° half angle cone at a wall-to-total temperature ratio of 0.1, M∞=7.4 and Re∞m=4.2×106 m−1, in terms of density fluctuations and the convection velocity of density disturbances. Experimental shock tunnel data are collected using a multi-foci Focused Laser Differential Interferometer (FLDI) to probe the boundary layer at several heights. In addition, a high-fidelity, time-resolved Large-Eddy Simulation (LES) of the conical flowfield under the experimentally observed free stream conditions is conducted. The experimentally measured convection velocity of density disturbances is found to follow literature data of pressure disturbances. The spectral distributions evidence the presence of regions with well-defined power laws that are present in pressure spectra. A framework to combine numerical and experimental observations without requiring complex FLDI post-processing strategies is explored using a computational FLDI (cFLDI) on the numerical solution for direct comparisons. Frequency bounds of 160 kHz <f<1 MHz are evaluated in consideration of the constraining conditions of both experimental and numerical data. Within these limits, the direct comparisons yield good agreement. Furthermore, it is verified that in the present case, the cFLDI algorithm may be replaced with a simple line integral on the numerical solution.
... It is commonly agreed that the main source for free flow disturbances in conventional supersonic and hypersonic wind tunnels is the radiation of acoustic waves from the turbulent boundary layer at the wind tunnel walls into the measurement section 15,16,17 . Accordingly, the measured shape of the PSD spectrum (Fig. 9b) is consistent with the FLDI results from other wind tunnels 14,18 . A comparison regarding the amplitude of the freestream disturbances is void, since the absolute value of the optical phase difference (∆s) depends on the individual measurement setup and thus the prerequisite for an objective evaluation is missing. ...
... Another reliable technique for measuring freestream disturbances in the impulse facilities is the Focused Laser Differential Interferometry (FLDI) technique. As a non-intrusive and laser diagnostic technique, free stream density fluctuations have been successfully measured in multiple impulse and conventional hypersonic ground test facilities [21][22][23][24][25][26]. This is primarily because of its high spatial and temporal resolution than other techniques. ...
... The density fluctuation levels are then deduced using the Gladstone-Dale relation and knowing some of the measured disturbance characteristics [26,[28][29][30]. As a further advancement, multi-point FLDI systems have been developed and used to measure the disturbance wave speed, thereby deducing freestream density fluctuations simultaneously [22,25,26]. ...
... In contrast, the trend is the opposite for the RMS of the density or pressure fluctuations normalised by the mean values (Ref Fig. 8(b and c) and Fig. 9b). A similar trend was observed in the studies carried out by Gillespie et al. [22] and Hildebrand et al. [43] when they measured freestream density fluctuations at different unit Reynolds number conditions. Nevertheless, noting that there is a 19 % uncertainty in the normalized parameter, the differences in the obtained values between these shots are within the uncertainty range. ...
